Monolayer transition-metal dichalcogenides are direct gap semiconductors with great promise for optoelectronic devices. Although spatial correlation of electrons and holes plays a key role, there is little experimental information on such fundamental properties as exciton binding energies and band gaps. We report here an experimental determination of exciton excited states and binding energies for monolayer WS2 and WSe2. We observe peaks in the optical reflectivity/absorption spectra corresponding to the ground- and excited-state excitons (1s and 2s states). From these features, we determine lower bounds free of any model assumptions for the exciton binding energies as E2sA - E1sA of 0.83 eV and 0.79 eV for WS2 and WSe2, respectively, and for the corresponding band gaps Eg >= E2sA of 2.90 and 2.53 eV at 4K. Because the binding energies are large, the true band gap is substantially higher than the dominant spectral feature commonly observed with photoluminescence. This information is critical for emerging applications, and provides new insight into these novel monolayer semiconductors.
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